The rank gradient from a combinatorial viewpoint

By Miklós Abért, A. Jaikin‐Zapirain, Nikolay Nikolov. 2007

67 citations recorded by the source corpus.

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups. As a tool for the amenable case we generalize Lackenby’s trichotomy theorem on finitely presented groups.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ada5cd5f6765da7249e088aa143b4cc81feb2248

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Alexander Lubotzky
2. Nikolay Nikolov
3. Miklós Abért
4. Rostislav I. Grigorchuk
5. Andreas Thom
6. Michael Larsen
7. Gareth Wilkes
8. A. Jaikin‐Zapirain

In Mathematical Physics

1. Alexander Lubotzky
2. Miklós Abért
3. Nikolay Nikolov
4. A. Jaikin‐Zapirain

Citations in the corpus

• Expander graphs in pure and applied mathematics (2011, background): “oups (except of D 1- the innite dihedral group for which clearly RG = 0) while amenable groups cannot contain free groups. This last corollary was extended to all nitely generated amenable groups in [AJN]. 48 Chapter 6 Expanders and Geometry In this chapter we describe several ways in which expander”
• Group cocycles and the ring of affiliated operators (2007, unknown): “This generalizes Proposition 5 in [1].”
• Rank gradient, cost of groups and the rank versus Heegaard genus problem (2007, background): “Note that in a joint paper [2] with A.”